Novel superconducting phases in copper oxides and iron-oxypnictides: NMR studies

We reexamine the novel phase diagrams of antiferromagnetism (AFM) and high-T_c superconductivity (HTSC) for a disorder-free CuO₂ plane based on an evaluation of local hole density (p) by site-selective Cu-NMR studies on multilayered copper oxides. Multilayered systems provide us with the opportunity to research the characteristics of the disorder-free CuO₂ plane. The site-selective NMR is the best and the only tool used to extract layer-dependent characteristics. Consequently, we have concluded that the uniform mixing of AFM and SC is a general property inherent to a single CuO₂ plane in an underdoped regime of HTSC. The T=0 phase diagram of AFM constructed here is in quantitative agreement with the theories in a strong correlation regime which is unchanged even with mobile holes. This Mott physics plays a vital role for mediating the Cooper pairs to make T_c of HTSC very high. By contrast, we address from extensive NMR studies on electron-doped iron-oxypnictides La1111 compounds that the increase in T_c is not due to the development of AFM spin fluctuations, but because the structural parameters, such as the bond angle α of the FeAs₄ tetrahedron and the a-axis length, approach each optimum value. Based on these results, we propose that a stronger correlation in HTSC than in FeAs-based superconductors may make T_c higher significantly.     

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.     

Triggered single-photon emission and cross-correlation properties in InAlAs quantum dot

Triggered single-photon generation from InAlAs quantum dot (QD) was demonstrated for the first time. Emitted photon energy coincides with high detection efficiency range of Si single-photon detectors, which is highly suitable for free-space communication. Single-QD spectroscopy and crossed photon correlation measurements unambiguously revealed that several emitting lines observed in a single mesa structure originated from the identical QD, and two temporary competing decay processes associated with neutral states and charged states were identified. Presence of the competing process is also inferred from an analysis of steady-state photoluminescence intensities. Formation process of charged exciton in QD is also discussed.     

Oblique interactions of weakly nonlinear long waves in dispersive systems

Studies on the oblique interactions of weakly nonlinear long waves in dispersive systems are surveyed. We focus mainly our concentration on the two-dimensional interaction between solitary waves. Two-dimensional Benjamin–Ono (2DBO) equation, modified Kadomtsev–Petviashvili (MKP) equation and extended Kadomtsev–Petviashvili (EKP) equation as well as the Kadomtsev–Petviashvili (KP) equation are treated. It turns out that a large-amplitude wave can be generated due to the oblique interaction of two identical solitary waves in the 2DBO and the MKP equations as well as in the KP-II equation. Recent studies on exact solutions of the KP equation are also surveyed briefly.     

Vibrational properties of noble gas endohedral fullerenes

Analysis of IR and Raman spectra of Ar@C(60) and Kr@C(60) shows that the incorporation of noble gas atoms causes a blue shift of low energy vibrations, which have radial character, and a red shift of higher energy ones which have a tangential character movement. The mechanism of these phenomena is explained on the basis of ab initio numerical experiments with DFT and MP2 procedures. Methodological discussions are advanced, altogether with a scheme for the estimation of the van der Waals interaction between fullerene and noble gas, based on the frequency shifts.     

Multiple gamma functions,multiple sine functions,and Appell’s <Emphasis Type="Italic">O</Emphasis>-functions

Kurokawa introduced q-multiple gamma functions and q-multiple sine functions. We show that the Appell’s O-function is expressed via the q-multiple gamma function. We also give some applications of this result. For example, we obtain a formula for the “Stirling modular form” and calculate special values of the q-multiple sine function. Moreover, we give some formulas of Eisenstein series and double cotangent functions and its generalization. Then the former gives an infinite product expression of the double sine function explicitly and a result of Kurokawa.     

Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations

Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.     

Synthesis of glycosaminoglycans via enzymatic polymerization

Hyaluronic acid and chondroitin were successfully synthesized as representative molecules of glucosaminoglycans and galactosaminoglycans found in a glycosaminoglycan family via enzymatic polymerization catalyzed by testicular hyaluronidases. A newly designed N-acetylhyalobiuronate oxazoline derivative with a β-D -glucuronyl-(1→3)-N-acetyl-D -glucosamine disaccharide structure served as a transition-state analogue substrate monomer for the enzyme, giving rise to artificial hyaluronic acid in 52% yields with a number-average molecular weight of 1.35 × 10⁴ through ring-opening polyaddition in a perfect regioselective and stereoselective manner. A novel N-acetylchondrosine oxazoline derivative with a β-D -glucuronyl-(1→3)-N-acetyl-D -galactosamine disaccharide structure also acted as a transition-state analogue substrate monomer for the enzyme, yielding artificial chondroitin in 35% yields with a number-average molecular weight of 2.5 × 10³. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3541–3548, 2003